Various works have introduced GPs to VAEs in order to overcome the i.i.d. assumption of the latent representations of VAEs. Casale et al. [1]} assumed a GP prior for the latent space of the VAE in order to incorporate the view and object information of the subjects. The GPPVAE model that they proposed assumes that the data is homogeneous (normally distributed). Moreover, its ability to model the subject-specific temporal structure is limited by the restrictive nature of the view-object GP product kernel.
Fortuin et al. [2]} proposed the GP-VAE model that assumes an independent GP prior on each subject's time series. The model cannot capture temporal correlations across different subjects, and it does not utilise the auxiliary covariate information other than time.
Ramchandran et al. [3]} proposed the L-VAE, which is a VAE-based model with a multi-output additive GP prior. L-VAE captures the structure of the low-dimensional embedding while utilising the auxiliary covariate information. They also proposed an efficient minibatch-based GP inference scheme. Even though L-VAE has a comprehensive capability to capture shared temporal structure as well as individual temporal structure with the help of auxiliary covariates, it assumes that the data is normally distributed, which is a major shortcoming in the modelling of longitudinal data.
Our model addresses these shortcomings while capturing the correlations among individual subjects and temporal dependencies. We handle the various challenges of incorporating heterogeneous data while effectively building on the benefits offered by GPs and VAEs. table:comparison compares our method with the prime related methods.
